A 50 meter path surrounds a rectangular garden. the width of the garden is two thirds it's length. find the length and width

W = 2L / 3 and 2W + 2L = 50. Substitute 2L / 3 for W in the second equation to get:

2 (2L/3) + 2L = 50

4L/3 + 6L/3 = 50

10L/3 = 50

L = 3 * 50 / 10 = 15. Replace L for 15 in the first equation:

W = 2 (15) / 3

W = 10

W = 2L / 3 and 2W + 2L = 50. Substitute 2L / 3 for W in the second equation to get : 2 (2L/3) + 2L = 50. 4L/3 + 6L/3 = 50